The quantum nature of the high temperature superconductivity models makes analytical approaches to these systems almost impossible to implement. In this thesis, a computational study of the one and two dimensional t − J models that combines mean-field treatments with renormalization group techniques will be presented. This allows one to deal with the noncommutations of the operators at two consecutive sites of the lattices on which these models are defined. The resulting phase diagram for the 1D t − J model reveals an antiferromagnetic ground state, which may, upon doping with increasing temperature, show striped formation that is seen in the high-Tc cuprates. The qualitative features of the phase diagram of the 2D case is also presented, which reveals a phase transition between the disordered and antiferomagnetically ordered phases.